This paper derives a procedure for simulating continuous non-normal distributions with specified L-moments and L-correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product-moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L-moment-based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L-skew and L-kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. Further, the L-correlation also demonstrated to be less biased and more stable than the Pearson correlation. It is also shown how the proposed L-moment-based procedure can be extended to the larger class of power method distributions associated with polynomials of order five.

This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate -moments and thecorrelations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of -skew, -kurtosis, and -correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also demonstrates that the estimates of -skew, -kurtosis, and -correlation are substantially superior to their conventional product moment-based counterparts of skew, kurtosis, and Pearson correlations in terms of relative bias and relative efficiency-most notably when heavy-tailed distributions are of concern.

<div id="titleAndAbstract"><p class="0abstract">Breast cancer poses the greatest threat to human life and especially to women's life. Despite the progress made in data mining technology in recent years, the ability to predict and diagnose such fatal diseases based on gene expression data still reveals a limited prediction performance, which may not be surprising since most of the genes in expression data are believed to be irrelevant or redundant. The dimensionality reduction process may be considered as a crucial step to analyze gene expression data, as it can reduce the high dimensionality of the breast cancer datasets, which may result into a better prediction performance of such diseases. The paper suggests a new hybrid approach-based gene selection that combines the filter method and the Ant Colony Optimization algorithm to find the smallest subset of informative genes (genes markers) among 24,481 genes. The proposed approach combines four machine learning algorithms - C5.0 Decision Tree, Support Vector Machines, K-Nearest Neighbors algorithm, and Random Forest Classifier - to classify each of the selected samples (patients) into two classes which have cancer or not.  Compared with existing methods in the literature, experimental results indicate that our proposed gene selection approach achieved globally higher classification accuracies with a relatively smaller number of genes.</p></div>

This paper introduces a standard logistic L-moment-based system of distributions. The proposed system is an analog to the standard normal conventional moment-based Tukey g-h, g, h, and h-h system of distributions. The system also consists of four classes of distributions and is referred to as (i) asymmetric -, (ii) log-logistic , (iii) symmetric , and (iv) asymmetric -. The system can be used in a variety of settings such as simulation or modeling events—most notably when heavy-tailed distributions are of interest. A procedure is also described for simulating -, , , and - distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that estimates of L-skew, L-kurtosis, and L-correlation associated with the -, , , and - distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias and relative standard error.

A characterization of Burr Type III and Type XII distributions based on the method of percentiles (MOP) is introduced and contrasted with the method of (conventional) moments (MOM) in the context of estimation and fitting theoretical and empirical distributions. The methodology is based on simulating the Burr Type III and Type XII distributions with specified values of medians, inter-decile ranges, left-right tail-weight ratios, tail-weight factors, and Spearman correlations. Simulation results demonstrate that the MOP-based Burr Type III and Type XII distributions are substantially superior to their (conventional) MOM-based counterparts in terms of relative bias and relative efficiency.

This paper introduces two families of distributions referred to as the symmetric κ and asymmetric - distributions. The families are based on transformations of standard logistic pseudo-random deviates. The primary focus of the theoretical development is in the contexts of L-moments and the L-correlation. Also included is the development of a method for specifying distributions with controlled degrees of L-skew, L-kurtosis, and L-correlation. The method can be applied in a variety of settings such as Monte Carlo studies, simulation, or modeling events. It is also demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when moderate-to-heavy-tailed distributions are of concern.

This paper introduces the Tukey family of symmetric h and asymmetric hh-distributions in the contexts of univariate L-moments and the L-correlation. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as modeling events e.g., risk analysis, extreme events and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when heavy-tailed distributions are of concern.

Objectives This study aims to investigate the feasibility and efficacy of competencybased course (Conceptual Geometry). In addition, this paper presents the procedures of developing competency‐based course which include mapping out competencies of the course, developing a set of assessment instruments (e.g., diagonal, pre‐and post‐unit assessments, CBL comprehensive pre‐and post‐assessments). Methods One hundred seventy‐nine graduate students who enrolled in a 5‐week Conceptual Geometry online course participated in this study. During the session, three sets of assessments were administered to assess the baseline of student knowledge (diagonal assessment), effectiveness (comprehensive pre‐and post‐assessments, and student content knowledge (5 sets of pre‐and post‐unit assessments). Results The results of this study showed that implementing an online CBL course is feasible and effective at a course level. Students showed higher scores on all of the post‐unit assessments (M = 95.45, SD = 4.62) than on the pre‐unit assessments (M = 69.42, SD = 7.77). This result supports the increase of student knowledge associated with geometry contents and pedagogy. The post‐comprehensive assessment results show an increase of student efficacy in geometry knowledge and skills using CBL course (pre‐assessment: M = 4.49, SD = 0.86; and post‐assessment: M = 5.14, SD = 0.40) which supports the increase of student efficacy of both content and pedagogical knowledge.